Question

sketch the right triangle and find the length of the side not given. (each length is in units.) leg = 35, hypotenuse = 91
sketch the right triangle. choose the correct answer below.
○ a. diagram with √35, √91, ?
○ b. diagram with 91, 35, ?
○ c. diagram with 35, 91, ?
○ d. diagram with 35, 91, ?
the unknown length is \\(\square\\) units.
(type a whole number or decimal rounded to the nearest thousandth as needed.)

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) are legs. Let \(a = 35\), \(c = 91\), find \(b\).
\(b^2 = c^2 - a^2\)

Step2: Substitute values

\(b^2 = 91^2 - 35^2\)
\(91^2 = 8281\), \(35^2 = 1225\)
\(b^2 = 8281 - 1225 = 7056\)

Step3: Solve for \(b\)

\(b = \sqrt{7056} = 84\)

Answer:

84